Trajectory optimization is a foundational aspect of a wellbore design. A deliberately optimized wellbore trajectory enables drilling to be performed under minimum geostress loads and promotes a longer service life for casings. Trajectory optimization is particularly significant to projects in which wellbores are designed with reference to a given platform. Although platform drilling has historically been an offshore consideration, an increasing number of field development designs include multiple wellbores drilled from a single surface location. Consequently, the necessity for trajectory optimization increases with the constraint of a fixed surface location to harvest a geometrically irregular reservoir.
All wells drilled for the purpose of oil/gas production (or injecting materials into underground formations) must be cased with material with sufficient strength and functionality. Casing and tubing strings are the main structural components of a wellbore design. Casing is needed to maintain borehole stability, prevent contamination of water sands, isolate water from producing formations, and control well pressures during drilling, production, and workover operations. Additionally, casing provides locations for the installation of blowout preventers, wellhead equipment, production packers and production tubing. The cost of casing is a major part of the overall well cost, so selection of casing size, grade, connectors, and setting depth is a primary engineering and economic consideration.
The fundamental basis of casing design is that if stresses in the casing pipe wall exceed the yield strength of the casing material, a failure condition exists. Hence, the yield strength is a measure of the maximum allowable stress on the casing pipe. To evaluate the pipe strength under combined loading conditions, the uniaxial yield strength is compared to the yielding condition. Perhaps the most widely accepted yielding criterion is based on the maximum distortion energy theory, which is known as Huber-Hencky-Mises yield condition and is more commonly referred to as “von-Mises stress.” Von-Mises stress is not a true stress. It is a theoretical value, which allows a generalized three-dimensional stress state to be compared with a uniaxial failure criterion (the yield strength). In other words, if the von-Mises stress exceeds the yield strength, a plastic yield failure is indicated.
The expression of von-Mises stress is stated as follows:
      σ    VME    =                    1                  2                    ⁢                                                  (                                                σ                  z                                -                                  σ                  θ                                            )                        2                    +                                    (                                                σ                  θ                                -                                  σ                  r                                            )                        2                    +                                    (                                                σ                  r                                -                                  σ                  z                                            )                        2                                ≥          Y      p      
where:
Yp=minimum yield strength
σVME=von-Mises stress
σz=axial stress
σθ=tangential or hoop stress
σr=radial stress.
While it is generally acknowledged that the von-Mises criterion is the most accurate method of representing elastic yield behavior, use of this criterion in tubular design often fails to consider that, for most pipe used in oilfield applications, collapse is frequently an instability failure, which occurs before the computed maximum von-Mises stress reaches the yield strength. Thus, the use of the von-Mises stress criterion is not appropriate. Only in thick-wall pipe does yielding occur before collapse. Additionally, the accuracy of an analysis using the von-Mises criterion is dependent upon the precise representation of the conditions that exist both for the pipe as installed in the well and for the subsequent loads of interest. Often, it is the change in load conditions that is most important in stress analysis. Thus, an accurate knowledge of all temperatures and pressures that occur over the life of the well can be critical to an accurate analysis using the von-Mises criterion.
In the past, attempts to better analyze casing failure using field scale and reservoir scale modeling has been difficult, if not impossible, due to the difficulty in combining the two models. In fact, existing examples of numerical analysis on casing failure were either performed at reservoir scale without direct coupling to behaviors at the field scale, or performed at a much larger scale, which sacrificed much needed modeling resolution.
There is therefore, a need for a method to numerically analyze casing failure both at the field scale and reservoir scale without sacrificing modeling resolution. Further, there is a need to consider additional parameters during the wellbore trajectory optimization process.